If a hyperbola passes through the point $\mathrm{P}(\sqrt{2}, \sqrt{3})$ and foci at $( \pm 2,0)$ then the tangent to this hyperbola at $\mathrm{P}$ is

Question

If a hyperbola passes through the point $\mathrm{P}(\sqrt{2}, \sqrt{3})$ and foci at $( \pm 2,0)$ then the tangent to this hyperbola at $\mathrm{P}$ is, $\mathrm{y}=\mathrm{x} \sqrt{6}-\sqrt{3}$, $\mathrm{y}=\mathrm{x} \sqrt{3}-\sqrt{6}$, $\mathrm{y}=\mathrm{x} \sqrt{6}+\sqrt{3}$, $y=x \sqrt{3}+\sqrt{6}$

MARKS App · Accepted Answer

Hint: $a e=2, a^2+b^2=4$ $\Rightarrow \frac{2}{a^2}-\frac{3}{b^2}=1 \Rightarrow b^2=3 ; a^2=1$ $\frac{x^2}{1}-\frac{y^2}{3}=1$. Tangent at $P(\sqrt{2}, \sqrt{3})$ is $\sqrt{6 x}-y=\sqrt{3}$

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